1. Field of the Invention
The invention relates to a signal processing method, apparatus, and program, which convert an N-dimensional input signal into an N-dimensional output signal of another sampling rate.
2. Description of the Related Art
Televisions and displays having high resolutions have prevailed. Upon displaying an image, a television or display converts the number of pixels of image data into that of a panel. Especially, in magnification that increases the number of pixels, as a method that can obtain an image sharper than linear interpolation, a method of reconstructing a high-resolution image using a plurality of pieces of frame information in consideration of inverse conversion of an image capturing process (deterioration process) is known (to be referred to as a reconstruction method hereinafter).
More specifically, for example, a block of several pixels squared (e.g., a block of 5 pixels in the horizontal direction×5 pixels in the vertical direction) is extracted from a low-resolution image to have a certain pixel as a center, and an area which has the same size as this block and includes pixels having pixel values close to those in the extracted block is searched in a frame to be converted. This search is conducted on the subpixel precision (for example, see M. Shimizu et al., “Precise Sub-pixel Estimation on Area-based Matching,” in Proc. IEEE International Conference on Computer Vision, pp. 90-97, 2001). After the search, the center of the found corresponding block is defined as a corresponding point. In this way, a point A corresponding to another frame and a point B corresponding to the frame to be converted are associated with each other as an identical position of an identical object. This associating algorithm will be referred to as a block matching method hereinafter. This association is expressed by a motion vector having the point A as a start point and the point B as an end point. Since the search is conducted on the subpixel precision, the start point of the motion vector is the position of a pixel, but the end point is generally a position where no pixel exists. Such a motion vector is calculated for all pixels of the low-resolution image, and motion vectors to the frame to be converted, which vectors have respective pixels as start points, are similarly detected from another low-resolution image. After the motion vectors to the frame to be converted are obtained, the pixel values of the start points are allocated at the end points of the respective motion vectors as sampling values of the frame to be converted. Finally, sampling values of pixels of a high-resolution image, which are uniformly allocated in a grid pattern, are calculated from sampling points which are non-uniformly allocated and sampling values at these points. Many methods of such conversion (reconstruction) have been proposed. For example, a non-uniform interpolation method, POCS (Projection Onto Convex Sets), an ML (maximum likelihood) estimator, and a MAP (maximum a posteriori) estimator are known (for example, see S. C. Park et al., “Super-Resolution Image Reconstruction: A Technical Overview,” IEEE Signal Processing Magazine, pp. 21-36, May 2003).
The method described as the related art searches for the position of a corresponding point for each pixel of another frame. Since no control is applied to a position found as a corresponding point, useless corresponding points are often found. Therefore, in order to find useful corresponding points, a method of using 10 to 30 other frames to double the vertical and horizontal resolutions needs to be used. Hence, the number of other frames needs to be increased to increase the chance of finding useful corresponding points.
Even when the number of frames is increased, no corresponding point often exists at an intermediate position with respect to a given low-resolution pixel. As a result, the estimation precision of a high-resolution image cannot be improved.